is there any Telegram bot out there which can send a private message to any member of a Group(where I am not the owner). If not, how would the procedure look like to build one?
That's not possible. For a bot to be able to send a message to a user, the user must have initiated a conversation with the bot first. Moreover, bots can't even get the list of members of groups or channels, especially not private ones (via the bot api).